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(Solved): Figure 1 shows a one-meter bar with non-insulating side surface. Students are required to identify a ...
Figure 1 shows a one-meter bar with non-insulating side surface. Students are required to identify a suitable non-linear ODE governing equation of the system and the NEUMANN Boundary Conditions. A reference must be cited and justified for the non-linear ODE in the Project 1 report.
a) The students must decide the number of nodes to be used to discretise the domain with equal distance, where the node number starts from "0" on the left boundary. Sketch the discretisation
- ???The students can choose either central, forward, or backward finite difference approximation of the second derivative. Rewrite the governing equation by substituting the second derivative finite difference approximation.
- ???After applying step b) to the discretised domain, write down all the equations.
- ???The boundary conditions must be incorporated into the equations.
- ???Then, assemble the equations in the form of a matrix equation.
Figure 1 shows a one-meter bar with non-insulating side surface. Students are required to identify a suitable non-linear ODE governing equation of the system and the NEUMANN Boundary Conditions. A reference must be cited and justified for the non-linear ODE in the Project 1 report. a) The students must decide the number of nodes to be used to discretise the domain with equal distance, where the node number starts from " 0 " on the left boundary. Sketch the discretisation. b) The students can choose either central, forward, or backward finite difference approximation of the second derivative. Rewrite the governing equation by substituting the second derivative finite difference approximation. c) After applying step b) to the discretised domain, write down all the equations. d) The boundary conditions must be incorporated into the equations. e) Then, assemble the equations in the form of a matrix equation.
Expert Answer
a) To discretize the domain with equal distances, the students need to determine the number of nodes to be used. Let's assume they decide on N nodes (including the endpoints), which means the distance between adjacent nodes is (1/N) meters. The node...